Optimal Production Management When Demand Depends on the Business Cycle

Abstract

We assume that the cumulative consumer demand for an item follows a Brownian motion, with both the drift and the variance parameters modulated by a continuous-time Markov chain that represents the regime of the economy. The management of the company would like to maintain the inventory level as close as possible to a target inventory level and would also like to produce at a rate that is as close as possible to a target production rate. The company is penalized for deviations from the target levels, and the objective is to minimize the total discounted penalty costs. We consider two models. In the first model the management of the company knows the state of the economy, whereas in the second model the management does not know it. We solve both problems and obtain the optimal production policy and the minimal total expected discounted cost. Furthermore, we compare the total expected discounted costs of the two models and determine the value of knowing the regime of the economy. We also solve the above problems in the case when the consumer demand rate follows a geometric Brownian motion modulated by a continuous-time Markov chain that represents the regime of the economy.